How can I see dmesg output as it changes?

Relatively recent dmesg versions provide a follow option (-w, --follow) which works analogously to tail -f.

Thus, just use following command:

$ dmesg -wH

(-H, --human enables user-friendly features like colors, relative time)

Those options are available for example in Fedora 19.

You can use the watch command which is intended exactly for things like this

watch -n 0.1 "dmesg | tail -n $((LINES-6))"

the $((LINES-6)) part should make it fit nicely into your terminal.

You can't really monitor the output of dmesg directly.

However, chances are high that your module is not printing directly into the ring-buffer of dmesg, but instead uses the kernel logging facilities (which will then be displayed by dmesg). If your syslog has some sane (e.g. default) settings, these messages will most likely also show up in the kern.log logfile.

So you can do something like:

 tail -f /var/log/kern.log